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melomori [17]
3 years ago
15

A thief steals an ATM card and must randomly guess the correct seven​-digit pin code from a 4​-key keypad. Repetition of digits

is allowed. What is the probability of a correct guess on the first​ try?
Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
7 0

Answer:

The probability of correct guess on the first​ try is \frac{1}{16384}.

Step-by-step explanation:

Consider the provided information.

The ATM has 4 key pad and required a 7 digit pin, where repetition is allowed.

Thief has 7 slots and 4 choices per slot. Because repetition is allowed.

Thus, the total number of different ways are:

4×4×4×4×4×4×4 = 16384

But only one combination is proper code.

Therefore,

\frac{1}{16384}

Hence, the probability of correct guess on the first​ try is \frac{1}{16384}.

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